A ___________________ is used in place of a number.


a.
Constant


b.
Variable


c.
Term


d.
Algebraic Expression

The slope of the line described in the table is m=3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The points from the table are (2, 6) and (3, 9)

Slope=9-6/3-2

=3/1

=3

Hence,  the slope of the line described in the table is m=3.

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Answer:

To find f(g(6)), we need to first find g(6) by plugging 6 into the function g(x) and solving for the output:

g(6) = 3x - 2 = 3 * 6 - 2 = 16

Next, we plug the result of g(6), which is 16, into the function f(x) and solve for the final output:

f(g(6)) = f(16) = 2x + 7 = 2 * 16 + 7 = 31

So f(g(6)) = 31.

E and F are the midpoints of AB and CD, respectively, making ABCD a parallelogram. Any line that crosses AD, EF, and BC at G, P, and H is designated as GH. So, GP = PH.

E and F are midpoints, resulting in AB and CD, respectively.

[tex]$\therefore \mathrm{AE}=\mathrm{BE}=\frac{1}{2} \mathrm{AB} \text { and } \mathrm{CF}=\mathrm{DF}=\frac{1}{2} \mathrm{CD}[/tex]

But, [tex]$\mathrm{AB}=\mathrm{CD}$[/tex]

[tex]$\therefore \frac{1}{2} \mathrm{AB}=\frac{1}{2} \mathrm{CD} \Rightarrow \mathrm{BE}=\mathrm{CF}[/tex]

Also, [tex]BE \| CF $\quad[\because \mathrm{AB} \| \mathrm{CD}]$[/tex]

therefore BEFC is a parallelogram.

[tex]$\Rightarrow \mathrm{BC} \| \mathrm{EF}$[/tex] and [tex]$\mathrm{BE}=\mathrm{PH}$[/tex]

Now, BC \| EF

[tex]$\Rightarrow \mathrm{AD} \| \mathrm{EF} \quad\left[\because \mathrm{BC} \| \mathrm{AD}\right.$[/tex] as ABCD is a [tex]$\left.\|^{\mathrm{gm}}\right]$[/tex]

[tex]$\Rightarrow \mathrm{AEF} \mathrm{D}$[/tex]is a parallelogram

[tex]$$\Rightarrow \mathrm{AE}=\mathrm{GP}$$[/tex]

But, [tex]\mathrm{E}$ is the mid-point of $\mathrm{AB}$[/tex]

[tex]\therefore \mathrm{AE}=\mathrm{BE}[/tex]

[tex]\Rightarrow \mathrm{GP}=\mathrm{PH} \quad$ [Using (i) and (ii)[/tex]

The complete question is:

ABCD is a parallelogram, E and F are the mid-points of AB and CD respectively. GH is any line intersecting AD, EF and BC at G,P and H respectively. Prove that GP = PH.

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We learn from the question that Johnny will need to buy 11 bags.

When you don't have much room, planters are a terrific choice since they let you showcase little trees and plants everywhere there is some sunshine. And you can still accept gardening and enjoy the benefits of raising your own food even if you just have a small patio, driveway, or balcony.

We'll start by determining the planter's volume. To achieve this, we'll calculate a triangular pyramid's volume:

Volume = (Ground Area x Altitude) / 3.

The planters measures 4 square feet in base area and 8 feet in height, so:

Volume = (4 x 8) / 3

Volume = 16 cubic feet

Now we know that Johnny needs 16 cubic feet of potting soil, and each bag of soil has 1.5 cubic feet, so:

Number of Bags = Volume / Volume per Bag

Number of Bags = 16 / 1.5

Number of Bags = 10.67

Since Johnny can't buy fractional bags of soil, he'll need to purchase 11 bags.

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Answer:

We start by calculating the discount amount for the extra 60% off with code SALE:

$29.99 * 60% = $17.99

Then we calculate the new price of the jeans after applying the discount:

$29.99 - $17.99 = $12

Next, we calculate the sales tax of 10.25% for the discounted price:

$12 * 10.25% = $1.23

Finally, we add the sales tax to the discounted price to find the final price:

$12 + $1.23 = $13.23

So the total cost of the jeans, with the extra 60% off code and sales tax of 10.25% included, would be $13.23.

The function is decreasing, is true about this function for all values of x < 4.

To develop a graph is to make a diagram that depicts the relationship between two or more objects. Make a sequence of bars on graph paper as an example of a graph.

A nonlinear graph can have more than one x-intercept, but it cannot have exactly two x-intercepts for all values of x. The vertex of a nonlinear graph is a special point that occurs when the graph changes from increasing to decreasing or vice versa, but it is not necessarily an x-intercept.

Therefore, the statement that the function intercepts the x-axis at points (2.8, 0) and (5.5, 0) with vertex point at (4, -2) is not true and decreasing for all values of x.

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Complete question:

Which statement is true about this function for all values of x < 4

The function is positive.

The function is decreasing.

The function is increasing.

The function is negative.

Answer:

Step-by-step explanation:

decimal equivalent of 714.45/9

divide it by 9 taking to 79.383333

Answer:

Michelle weighs 120.15 lb. now.

You can calculate it by

145lb x (1-.17) = 145lb x .83 = 120.15lb

So right now in the the given question we use the proportional method

In this case the proportion used is inverse

In direct proportion, if one quantity is increased or decreased then the other quantity increases or decreases, respectively. But in indirect or inverse proportion, if one quantity increases then other quantity decreases and vice-versa.

Eg: As the variable y decreases the variable x will also decrease

When we apply the given values into a fraction we get

[tex]\frac{18}{72} = \frac{13}{x}[/tex]

Cross Multiplying we get,

[tex]18x = 72X13[/tex]

[tex]18x = 936[/tex]

[tex]x = \frac{936}{18}[/tex]

[tex]x = 52[/tex]

Hence, 13 inches of wire costs 52 cents

Answer:

x - 9.9 = 31.6

If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be [tex]$x=-\frac{2}{3}, x=-\frac{5}{2}$$[/tex].

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.

Area of rectangle = length × breadth

= (3x +2) × (4x +10)

simplifying the above equation, we get

= (3x) × (4x +10) + 2(4x +10)

= 12x² + 30x +8x +20

12x² + 38x + 20 = 0

simplifying the above equation, we get

By using quadratic equation, then

[tex]$x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$[/tex]

simplifying the above equation, we get

[tex]$$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$[/tex]

Separate the solutions, we get

[tex]$$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$[/tex]

The solutions to the quadratic equation are:

[tex]$x=-\frac{2}{3}, x=-\frac{5}{2}$$[/tex]

The complete question is:

Find the area of rectangle with length (3x+2) units and width (4x+10)units.

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A table of equivalent ratios for the number of toss and amount of dollars is as follows:

Toss             Dollars

25                    4

50                    8

75                    12

In order to have a proportional relationship and equivalent ratios, the variables x for toss and y for dollars must have the same constant of proportionality.

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = y/x

Constant of proportionality (k) = 12/75

Constant of proportionality (k) = 0.16.

When hours y = 8, the amount of dollars x is given by:

x = y/k

x = 8/0.16

x = 50.

When the amount of dollars x = 25, the number of toss y is given by:

y = kx

y = 0.16(25)

y = 4.

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Answer:

971.92 square inches of wrapping paper.

Step-by-step explanation:

Please find the attachment for detail

The t-test for independent groups is usually the most sensitive test when there is large between-subject variability and the sample size (N) is held constant.

The t-test for independent groups allows for the comparison of two independent groups, and can detect differences in the means between the two groups that may not be detected by other tests. The t-test for correlated groups is less sensitive than the t-test for independent groups, as it assumes that the two groups are related or correlated. The sign test is a non-parametric test and is less sensitive than the t-test for independent groups as it does not take into account the variability between the two groups.

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The probability that can be determined by the randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.

Given information is that, at a wedding, each guest asked the 80 guests if they were a friend of the bride or of the groom.

Probability is measured by the ratio of the number of favorable outcomes to the total number of outcomes of an event.

The total Number of Guests which forms the Sample Space, n(S)=80

Let the event for a friend of the bride=A

Let the event be for a friend of the groom=B

n(A) =59

n(B)=50

Friends of both bride and groom,

So,

n(A∪B)=n(A)+n(B)-n(A∩B)

n(A∪B)=59+50-30

n(A∪B)=79

The number of people or Guests who are the friends of the bride OR of the groom = 79

Thus,

P(A∪B)=n(A∩B)/n(S)

= 79/80

P(A∪B)= 0.9875

Therefore, the probability that a randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.

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The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Pizza sales increase by 8% this year then decrease by 4%. Then we have

P = [1 - (1 + 0.08) x (1 - 0.04)] x 100

P = [1 - 1.08 x 0.96] x 100

P = [1 - 1.0368] x 100

P = [1 - (1 + 0.0368)] x 100

P = 0.0368 x 100

P = 3.68%

The percentage that your sales are up will be 3.68%.

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The total amount present in the account is  $555 in 5 years with a rate of 2.2%.

Simple interest is a way to figure out how much interest will be paid on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the following year's principal to compute interest, the principal amount under simple interest remains constant.

Simple interest is a quick and simple approach to figure out how much money has accrued interest. Interest is always applied to the initial principle amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of several forms of interest that banks charge.

It is given The initial Principal is $500

The interest earned is $55

The total amount present in the account is $(500 + 55) = $555 in 5 years

The rate of interest is r(say)

principal * rate * time = interest

⇒500* r * 5 = 55

⇒ r = 0.022 = 2.2 %

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The 15th percentile can be found to be 66.5

The value that a specific percentage falls under is known as the percentile. The most typical definition of a percentile is a number below which a predetermined proportion of scores fall.

To find the 15 th percentile, the formula is:

= ( Percentile / 100 )  x Number of values in set

The 15th percentile is therefore:

= 15 / 100 x 117

= 17.55

= 18 th position

The value in the 18th position which is the 15th percentile is 66.5

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The length x of a side of the small inner square in terms of some of the variables a , b is expressed as x = (b - a).

We have, length x which is side of inner square in above figure. We have to determine the value of x in terms of " a and b." See the figure carefully and draw the important results. As we see,

Also, see in above figure, the side length of blue triangle is equals to the sum of side length of yellow triangle and side length inner square. In expression form , b = x + a . But we want to determine the value of x, so x = b - a.

Hence, required length is ( b - a).

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Complete question:

what is the length x of a side of the small inner square? express your answer in terms of some or all of the variables a , b , and c.

The above figure complete the question.

Answer:

below

Step-by-step explanation:

When y = 0    the negative x value of the vertex needs to be a negative number ....the second equation will do this...the first will not

The equation of the parabola with given vertex and focus is (y-11)² = 36(x-7).

A parabola refers to an equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line.

The general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h, where (h, k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.

Given that, Vertex (7, 11), focus (16, 11).

Let us find an equation of the parabola for vertex (h, k)=(7, 11) and focus (16, 11).

It can be observed that both focus and vertex lie on y = 11, thus the axis of symmetry is a horizontal line.

a = 16-7 = 9 as y coordinates are the same.

Since the focus lies to the left of vertex, a = 9

Use the equation (y-11)² = 4×9(x-7)

(y-11)² = 36(x-7)

Therefore, the equation of the parabola with given vertex and focus is (y-11)² = 36(x-7).

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The standard equation of the parabolas with vertex (7, 11) and focus (16, 11) are:

(y - 11)² = 36(x - 7)

A parabola is an equation of a curve, such that any point on the curve is equidistant from a fixed point called the focus and a fixed line called the directrix of the parabola.

We have,

(y - k)² = 4p (x - h) open right

(y - k)² = -4p (x - h) open left

Where focus = (h - p, k)  or (h + p, k) and vertex = (h, k)

Now,

Equation of parabola (y - k)² = -4p (x - h) that open left.

(h, k) = (7, 11)

h = 7 and k = 11

(h - p, k) = ( 16, 11)

h - p = 16

7 - p = 16

7 - 16 = p

p = -9

So,

(y - 11)² = 36(x - 7)

Equation of parabola (y - k)² = 4p (x - h) that open right.

(h, k) = (7, 11)

h = 7 and k = 11

(h + p, k) = (16, 11)

h + p = 16

7 + p = 16

p = 16 - 7

p = 9

So,

(y - 11)² = 36 (x - 7)

Thus,

The standard equation of the parabolas is:

(y - 11)² = 36(x - 7)

(y - 11)² = 36 (x - 7)

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Answer:

In order to find the probability that a pupil selected at random obtained more than 27 marks, we need to know the total number of pupils and the number of pupils who scored more than 27 marks.

Let's call the total number of pupils "n" and the number of pupils who scored more than 27 marks "x".

From the given data, we know that n = 6 and the pupils who scored more than 27 marks are 39, 40, 37.

x = 3

Now we can use the formula for probability:

Probability = (x/n)

Probability = (3/6)

Probability = 0.5

So the probability that a pupil selected at random obtained more than 27 marks is 0.5 or 50%.

Step-by-step explanation:

Answer:

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.

To find the equation of the line with a slope of 2/3 and passing through the point (3, -4), we can plug in the point and the slope into the equation:

y = 2/3 * x + b

-4 = 2/3 * 3 + b

-4 = 2 + b

b = -6

So the equation of the line is:

y = 2/3 x - 6

Answer:

B

Step-by-step explanation:

[tex](x-1)(x+1) = x^2 -1\\(x+5)(x-5) = x^2 -25[/tex]

The missing 3 steps for the given equivalent equation are as follows:

1st step: 2x - 6 = 4x

2nd step: -6 = 2x

3rd step: -3 = x

Algebraic equations with equivalent solutions or roots are called equivalent equations.

An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation.

An equation is equivalent if both sides are multiplied or divided by the same non-zero value.

So, we have the equation:

2(x-3) = 4x

Now, solve further as follows:

2(x-3) = 4x

1st step: 2x - 6 = 4x

2nd step: -6 = 2x

3rd step: -3 = x

Therefore, the missing 3 steps for the given equivalent equation are as follows:

1st step: 2x - 6 = 4x

2nd step: -6 = 2x

3rd step: -3 = x

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Answer:

4000cm

Step-by-step explanation:

1m is equal to 100cm

so 400m is equal to 400 x 10 which is 4000

so 1cm dividided by 400m ks 400m

Answer:

≈ +1

Step-by-step explanation:

Firstly, the r value, or the correlation coefficient, would be positive because the correlation is positive. The set of points are moving from bottom to top.

It would be close if not exactly to 1 because the closer the set of points are all clustered closely around or on one singe line, the closer it is to 1. In this case, all points seem to be on one single line, suggesting that it has a perfect correlation of 1.

Answer:

x = 12

y = -2.5

Step-by-step explanation:

2x + 4 = 28

2x = 24

x = 12

So, we know x = 12; now we put 12 back in for x and solve for y

3(12) + 4y = 26

36 + 4y = 26

4y = -10

y = -2.5

Let's check

3(12) + 4(-2.5) = 26

36 - 10 = 26

26 = 26

So, x = 12 and y = -2.5 is the correct answer.

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

we have here 3 triangle sides.

the painter can only paint the sides, not the base area.

the painting area is therefore the sum of the 3 sides :

3× 50×40/2 = 3× 50×20 = 3000 ft²

75% of the area = 3000 × 0.75 = 2250 ft²

100 ft² in 18 minutes

it takes

2250/100

times of the time it takes to paint 100 ft² (18 minutes).

so,

18 × 2250/100 = 405 minutes

it takes the painter 405 minutes to paint 75% of the pyramid.

The d f of 8 for the following equation  is-   7698

f₍ₓ₎ = ᵃˣ²+ᵇˣ²+c

f₍₀₎ = a*0²+b*0+c = 2

   = 0+0+c=2

  c=2

f₍₃₎ = a(3)²+b*3+c = 128

    = 9a + 3b +2 = 128

   = 9a+3b = 128-2

    9a+3b = 126    equation  (i)

f₍₅₎ = a (5)² + b*5 + c = 2048    = 25a + 5b + 2 = 2048

     25a+ 5b = 2046    equation ( ii)

equation (ii) is multiplied by 3 and equation (i) multiplied by 5  we get,

       25a+ 5b = 2046

           9a+3b = 126  

Subtracting equation (ii) from equation (i)

          75a + 15b  = 6138

          45a + 15b = 630

          30a        = 5508

       a = 5508/30

         a  = 184

 now , putting the value of a in equation (i)

     9*184+3b+2  = 128

      1656+3b +2 = 128

   3b = 128-1658

    b = -510

f₍ₓ₎ = 184 x² - 510x + 2

  = 184*64 - 510*8 +2

  = 11776 - 4080+2

  = 7698 ans.

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